Aspects of performance And Application Fields

AbstractIn wireless communication, the received signal is distorted one from the transmitted signal due to the Inter-Symbol Interference (ISI). This problem can be overcome using channel equalization which is an adaptive filtering that approximately inverse the channel effect. This paper analyze the performance of the Least Mean Square (LMS) algorithm equalizer and the Constant Modulus Algorithm (CMA) equalizer in terms of the convergence speed and the error rate based on a unified error function, since they have different cost functions. And also determine the application field for these two equalizers. Quadrature Phase Shift Keying (4QPSK) is used as a modulation technique.

Index TermsAdaptive equalizer, LMS, Constant Modulus Algorithm(CMA), convergence, phase modulation.


VERY wireless communication system encounter the Inter-Symbol Interference problem which is a result of multipath effect and limited bandwidth of the practical channel. Due to this phenomenon the received signal is a distorted one from the transmitted signal. This problem can be overcome using channel equalization which is a filter that approximately inverse the channel effect; in time-varying channels an adaptive algorithm is needed to update the filter taps.

Conventional LMS adaptive equalizers use known training data that used as a desired signal to the adaptive algorithm while CMA introduces a different cost function that exploits the characteristics of the transmitted modulated signal.

This paper focuses on the analysis of the performance of the Least Mean Square (LMS) equalizer and the Constant Modulus Algorithm (CMA) equalizer. For the sake of the analysis study the Quadrature Phase Shift Keying (4-QPSK) is used as a modulation technique and a unified error function is introduced since the two algorithms have different cost functions functions and hence each one has different error function; as a conclusion, the appropriate application fields are determined.

Review of the State of Art

It has been demanding to come up with a technique that does not require the availability of these training data; this technique is called blind channel equalization. Godard proposed in [1] the algorithm that can be used for this purpose. This algorithm introduces a different cost function that exploits the characteristics of the transmitted modulated signal. Godard's algorithm works for phased-modulated signal as it has a constant modulus therefore it is called Constant Modulus Algorithm (CMA).

In [2], four different versions of CMA have been presented that derived from the same cost function introduced by Godard, and a modified algorithm was proposed.

In [3], the fundamental concepts about equalizers, blind channel equalization and constant modulus algorithm have been presented. Also a new algorithm had been proposed and its performance compared with CMA.

Problem Statement and Main Contribution

The problem of ISI in wireless communication systems can be solved by using adaptive equalizers at the receiver side depending on the way in which we transmit the data. The key Question arises, how we can determine the appropriate application filed of LMS based equalizers and CMA based equalizers.

By analysis of the performance based on a unified error function in terms of convergence speed and the error rate generated according to the proposed error function we can determine the application fields for the two different equalizers.

The main contributions of the paper are:

  1. Implement two equalizers models based on the two algorithms.
  2. Analysis of the two equalizers over the error rate and the convergence speed based on the simulation results.

Problem Solution

Simulation process :

In this project Matlab 7 is used as a simulation tool model b(n) is the binary signal that represents the digital data. The binary data is then modulated using QPSK technique to produce the transmitted signal s (n). s (n) goes through the channel that has the transfer function H(z) according to [2].and thus the receiver gets the signal which is now referred as x (n) or the received signal. The objective of equalizer is to cancel the channel effect on the transmitted signal and thus obtain and estimate which is given as the output of the equalizer y (n). The number of filter coefficients is 5 with 150,000 transmitted samples. For CMA algorithms, the constant R is set to 1. The simulation was performed in Matlab 7.0.

Result & analysis:

Fig.1. present the transmitted signal which is a QPSK modulated signal; also the received signal which is the transmitted signal passed through the distortion channel. While fig.2. Shows the equalized signals represent the received signal filtered by the adaptive LMS equalizer and CMA respectively.


From the obtained results it can be concluded that CMA algorithms much slower than LMS algorithm and also may have higher minimum error. It can also be concluded from the simulation that the initialization of the CMA algorithm has significant effect in the convergence as it has non-convex cost function. From above, the blind channel equalization can be used whenever no training data is available. In addition to that, it also can be used when it is demanded to increase the throughput of the system while the convergence speed and the minimum error can be compromised.

For the future work, to find a hypered algorithm that exploits the merits of the two algorithms is highly recommended.


The authors would like to thank prof. Woldek Kulesze for his constant support and guidance through the preparation of this paper; without his help this research article would have never been ameliorated.


  1. GODARD, Dominique N, "Self-Recovering Equation and Carrier Tracking in Two-Dimensional Data Communication Systems," No. 11, IEEE TRANSACTIONS ON COMMUNICATIONS, November 1980, Vols. COM -28.
  2. Jones, Douglas L, "A Normalized Constant-Modulus Algorithm," IEEE Proceedings of ASILOMAR -29, 1996.
  3. Norfizah Md. Ali, Jewel Aich," A Comparison of Sato and CMAAlgorithm in Blind Equalization and Identification of Communication Channels," PROCEEDINGS OF WORLD ACADEMY OF SCIENCE, ENGINEERING ANDTECHNOLOGY VOLUME 38 FEBRUARY 2009 ISSN:2070-3740.
  4. Nordberg, Jrgen, "Blind Subband Adaptive Equalization," Research Report, Blekinge Institute of Technology, 2002.

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